Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                  <s xml:id="N2B9C0" xml:space="preserve">
                    <pb chead="De intenſione difformium" file="0269" n="269"/>
                  Sed iã probo /  illa qualitas que extendit̄̄ pro to-
                    <lb/>
                  tum prīo denoīat aliq̈liter et q̄ ꝑ totū reſiduū a pri­
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                  ma in f. ꝓportione minꝰ ꝙ̄ illa q̄ extēditur ꝑ totum:
                    <lb/>
                  et ſic ↄ̨ñten. </s>
                  <s xml:id="N2B9CD" xml:space="preserve">Qm̄ oēs ille qualitates ſunt equalis
                    <lb/>
                  intēſionis: et q̄libet ſequēs ꝑ minꝰ in f. ꝓportiõe ex-
                    <lb/>
                  extēdit̄̄ ꝙ̄ precedēs: qm̄ totū illud corpus eſt in f. ꝓ­
                    <lb/>
                  portiõe maius ꝙ̄ totū aggregatū ex oībus ꝑtibus
                    <lb/>
                  ꝓportionalibꝰ eius ſequētibus primã: et totū reſi-
                    <lb/>
                  duū a prima eſt in f. ꝓportiõe maius toto reſiduo a
                    <lb/>
                  prīa et ſcḋa: et ſic ↄ̨ñter: vt pꝫ ex prīa cõcluſione quin­
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                  ti capitis prime partis: hoc addito /  quacū pro­
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                  portiõe diuidit̄̄ totū eadē proportõe diuidit̄̄ aggre­
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                  gatū ex oībus ꝑtibus ꝓportionalibꝰ ſequētibꝰ pri­
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                  mã: et etiã ſequētibꝰ ſcḋam: et tertiã: et q̈rtã: et ſic ↄ̨ſe­
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                  quenter: igr̄ illa qualitas q̄ ꝑ totū extenditur deno­
                    <lb/>
                  minãt aliquãtulū: et q̄ ꝑ totuꝫ reſiduū a prīa in f. ꝓ­
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                  portiõe minꝰ: et q̄ per totū reſiduū a ṗma et ſecūda
                    <lb/>
                  in f. ꝓportiõe minꝰ ꝙ̄ illa q̄ per totū reſiduū a prīa /
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                  et ſic ↄ̨ñter / qḋ erat ꝓbandū </s>
                  <s xml:id="N2B9EE" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ ſecundã
                    <lb/>
                  partē prīe ꝓpõnis vltimi notabilis.
                    <note position="left" xlink:href="note-0269-01a" xlink:label="note-0269-01" xml:id="N2BB32" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N2B9F8" xml:space="preserve">
                    <gap/>
                  Ex hac ↄ̨clu-
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                  ſione ſeq̇tur prīo /  ſi aliqḋ corpus diuidatur ꝑ par­
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                  tes ꝓportionales ꝓportiõe tripla: et ṗma pars ꝓ-
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                  portionalis eiꝰ ſit aliquaĺr intenſa: et ſcḋa ī duplo
                    <lb/>
                  et tertia in triplo plus ꝙ̄ ṗma cõtinuo eadē qualita­
                    <lb/>
                  te: et ſic ↄ̨ñter: ſine aliqua ↄ̈rii admixtione: totū ē in
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                  ſexquialtero intenſius ṗma parte ꝓportionali. </s>
                  <s xml:id="N2BA08" xml:space="preserve">Et
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                  ſi diuidat̄̄ corpꝰ ꝓportiõe quadrupla totū erit intē­
                    <lb/>
                  ſius prima parte ꝓportionali in ſexq̇tertio. </s>
                  <s xml:id="N2BA0F" xml:space="preserve">Et ſi ꝓ-
                    <lb/>
                  portiõe quītupla: erit intēſius prīa parte ꝓportio-
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                  nali in ſexq̇quarto. </s>
                  <s xml:id="N2BA16" xml:space="preserve">Et ſi ſextupla in ſexq̇quīto. </s>
                  <s xml:id="N2BA19" xml:space="preserve">Et ſi
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                  ſeptupla in ſexq̇ſextor / et ſic ↄ̨ñter ꝓcedēdo ꝑ ſpecies
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                  ꝓportõis multiplicis et ſuꝑparticularis. </s>
                  <s xml:id="N2BA20" xml:space="preserve">Probat̄̄ /
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                  hoc correlariū: q2 corpus diuiſum ꝓportiõe tripla
                    <lb/>
                  ſe hꝫ ad primã ꝑtē ꝓportionalē eius in ꝓportiõe ſex­
                    <lb/>
                  quialtera: et diuiſum quadrupla ſe hꝫ ad p̄mã par-
                    <lb/>
                  tē proportionalē in ꝓportiõe ſexq̇tertia: et diuiſum
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                  quintupla ſe hꝫ ad primã partē ꝓportionalē in ꝓ-
                    <lb/>
                  portione ſexq̇quarta: et ſic ↄ̨ñter: vt pꝫ ex primo cor­
                    <lb/>
                  relario tertie ↄ̨°nis quīti capitis prime partis: igr̄
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                  in caſu correlarii ſequit̄̄ ſi diuidat̄̄ corpus ꝓportio­
                    <lb/>
                  ne tripla  ip̄m erit intēſius prima parte ꝓportio­
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                  nali in ſexq̇altero: et ſi quadrupla ī ſexq̇tertio: et ſi
                    <lb/>
                  quintupla in ſexq̇quinto: et ſic ↄ̨ñter. </s>
                  <s xml:id="N2BA39" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ
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                  cõcluſioneꝫ.
                    <note position="left" xlink:href="note-0269-02a" xlink:label="note-0269-02" xml:id="N2BB38" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N2BA43" xml:space="preserve">¶ Seq̇tur ſcḋo /  ſi diuidat̄̄ corpus per
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                  partes ꝓportiõales proportõe dupla et diſtribuat̄̄
                    <lb/>
                  aliqua intēſio ꝑ illas partes ꝓportionales / vt po-
                    <lb/>
                  nitur in p̄cedēti correlario: tūc totū eſt in duplo in-
                    <lb/>
                  tenſius prīa ſui ꝑte ꝓportionali. </s>
                  <s xml:id="N2BA4E" xml:space="preserve">Probat̄̄ / q2 totuꝫ
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                  diuiſum per partes ꝓportionales ꝓportiõe dupla
                    <lb/>
                  eſt duplū ad primã partē ꝓportionalē eiꝰ / vt ptꝫ ex
                    <lb/>
                  primo correlario tertie ↄ̨cluſionis prime partis p̄-
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                  allegato: igr̄ ꝑ cõcluſionē illud eſt intēſius ſuã prīa
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                  parte ꝓportionali in ꝓportiõe dupla.
                    <note position="left" xlink:href="note-0269-03a" xlink:label="note-0269-03" xml:id="N2BB3E" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N2BA60" xml:space="preserve">¶ Sequitur
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                  tertio /  diuiſo corpore ſic ꝑ partes ꝓportionales
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                  ꝓportione dupla etc. / vt ponit̄̄ in añti correlario to-
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                  tū eſt ita intenſum ſicut ſcḋa ꝑs ꝓportionalis eius.
                    <lb/>
                  </s>
                  <s xml:id="N2BA6A" xml:space="preserve">ꝓbat̄̄ / q2 in duplo intēſiꝰ prīa vt p̄cedēs correlariū
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                  oſtēdit: et ſcḋa ꝑs ꝓportionalis ē eēt in duplo ītēſior
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                  prima: g̊ totum eſt ita intenſum ſicut ſcña pars pro­
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                  portionalis / quod fuit probandum. </s>
                  <s xml:id="N2BA73" xml:space="preserve">Patet cõſequē­
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                  tia per hanc maximam habentia equalem propor­
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                  tionem ad vnum tertium ſunt equalia. </s>
                  <s xml:id="N2BA7A" xml:space="preserve">Et hec eſt pri­
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                  ma concluſio calculatoris in capite de difformibꝰ.
                    <lb/>
                    <note position="left" xlink:href="note-0269-04a" xlink:label="note-0269-04" xml:id="N2BB44" xml:space="preserve">4. correĺ</note>
                  </s>
                  <s xml:id="N2BA86" xml:space="preserve">¶ Sequitur quarto /  ſi aliquod corpus diuidatur
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                  proportione ſexquialtera: et prima pars propor-
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                  tionalis ſit aliqualiter intenſa: et ſecunda in duplo
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                  plus: et tertia in triplo ꝙ̄ prima: et ſic conſequenter /
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                  vt
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                  ̀ concluſionis: tunc totum eſt in
                    <cb chead="De intenſione difformium"/>
                  triplo intenſius prima parte proportionali. </s>
                  <s xml:id="N2BA96" xml:space="preserve">Et ſi
                    <lb/>
                  diuidatur ꝓportiõe ſexquitertia: totum erit inten-
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                  ſius prima parte proportionali in quadruplo. </s>
                  <s xml:id="N2BA9D" xml:space="preserve">Et
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                  ſi diuidatur ꝓportione ſexquiquarta totum erit in­
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                  tenſius prima parte ꝓportionali in quintuplo. </s>
                  <s xml:id="N2BAA4" xml:space="preserve">Et
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                  ſi ſexquiquinta totum erit intenſius prima parte ꝓ­
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                  portionali in ſextuplo. </s>
                  <s xml:id="N2BAAB" xml:space="preserve">Et ſi ſexq̇ſexta in ſeptuplor /
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                  et ſic cõſequēter ꝓcedendo cõtinuo ꝑ ſpecies propor­
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                  tionis ſuperparticularis in diuiſione corporis: et
                    <lb/>
                  per ſpecies ꝓportionis multiplicis ex parte inten-
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                  ſionis. </s>
                  <s xml:id="N2BAB6" xml:space="preserve">Probatur hoc correlariū: quia totum diui­
                    <lb/>
                  ſum proportione ſexquialtera eſt triplum ad pri-
                    <lb/>
                  mam partem ꝓportionalē eius et diuiſum ſexq̇ter-
                    <lb/>
                  tium eſt quadruplū: et ſexquiquarta eſt quintupluꝫ
                    <lb/>
                  et ſexq̇quinta ſextuplū ad primã eius partē ꝓpor-
                    <lb/>
                  tionalē: vt pꝫ ex quarta cõcluſiõe quinti capitis pri­
                    <lb/>
                  me partis: g̊ in eiſdē ꝓportionibus ſe habēt inten-
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                  ſiones totius ad intenſionē prime partis ꝓportio­
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                  ntialis / vt patet ex cõcluſione: igr̄ correlariū verum
                    <lb/>
                  </s>
                  <s xml:id="N2BACA" xml:space="preserve">¶ Sequitur quīto /  ſi diuidatur corpus / vt dicitur
                    <lb/>
                  in precedēti correlario: vt puta ꝓportiõe ſexq̇alte-
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                  ra et prima pars ſit aliqualiter intēſa: et ſecūda in
                    <lb/>
                  duplo plus: et tertia ī triplo plus ꝙ̄ prima etc. / vt ibi
                    <lb/>
                  dicitur: totū eſt ita intenſū ſicut tertia pars ꝓpor-
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                  tionalis. </s>
                  <s xml:id="N2BAD7" xml:space="preserve">Et ſi ꝓportione ſexquitertia: ſicut quarta
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                  ꝑs ꝓportionalis. </s>
                  <s xml:id="N2BADC" xml:space="preserve">Et ſi ſexq̇quarta ſicut quinta ꝑs
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                  ꝓportionalis. </s>
                  <s xml:id="N2BAE1" xml:space="preserve">Et ſi ſexquiq̇nta ſicut ſexta pars ꝓ-
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                  portionalis: et ſic ↄ̨ñter deſcendendo per partes ꝓ-
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                  portionales et ꝑ ſpecies proportionis ſuperparti­
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                  ticularis in infinitum. </s>
                  <s xml:id="N2BAEA" xml:space="preserve">Probatur / quoniam ſi cor-
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                  pus ſit diuiſum proportione ſexquialtera ipſuꝫ eſt
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                  in triplo intenſius prima parte eius ꝓportionali /
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                  vt patet ex precedenti correlario: et tertia pars pro­
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                  portionalis eſt etiam in triplo intenſior prima / vt
                    <lb/>
                  patet ex caſu: ergo ita intenſum eſt tale corpus ſi-
                    <lb/>
                  cut tertia pars proportionalis. </s>
                  <s xml:id="N2BAF9" xml:space="preserve">Item ſi diuidatur
                    <lb/>
                  proportione ſexquitertia ipſum eſt in quadruplo
                    <lb/>
                  intenſius prima eius parte proportionali ex pre-
                    <lb/>
                  cedēti correlario. </s>
                  <s xml:id="N2BB02" xml:space="preserve">et etiã quarta pars proportiona­
                    <lb/>
                  lis eius ē in quadruplo intenſior prima ex caſu: igi­
                    <lb/>
                  tur illud corpus ita diuiſuꝫ proportione ſexquiter­
                    <lb/>
                  tia eſt ita intenſum ſicut quarta pars proportiona­
                    <lb/>
                  lis eius. </s>
                  <s xml:id="N2BB0D" xml:space="preserve">Et iſto modo ꝓbabis ceteras ꝑticulas cor­
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                  relarii. </s>
                  <s xml:id="N2BB12" xml:space="preserve">¶ Sequitur ſexto /  ſi aliquod corpus diui­
                    <lb/>
                  datur ꝑ partes ꝓportionales ꝓportione ſuprabi-
                    <lb/>
                  partiente tertias et ꝑtes eiꝰ ſint intēſe vt ſepiꝰ dcim̄
                    <lb/>
                  eſt totū erit intēſiꝰ prīa ꝑte ꝓportionali ī ꝓportiõe
                    <lb/>
                  dupla ſexq̇altera: ita  ſi prima ſit calida vt .2. to-
                    <lb/>
                  tum eſt calidum vt .5. </s>
                  <s xml:id="N2BB1F" xml:space="preserve">Probat̄̄ correlariū / qm̄ totū
                    <lb/>
                  eſt intenſiꝰ prīa ꝑte ꝓportionali in tali caſu in pro­
                    <lb/>
                  portione qua ſe habet aliqḋ totū diuiſum ꝑ ꝑtes ꝓ­
                    <lb/>
                  portionales ꝓportiõe ſuprabiꝑtiēte tertias ad ſuã
                    <lb/>
                  primã ꝑtē ꝓportionalē / vt pꝫ ex ↄ̨°ne: ſꝫ talis ē ꝓpor­
                    <lb/>
                  tio dupla ſexq̇altera / vt pꝫ intelligēti .5. cõcluſioneꝫ
                    <lb/>
                  quinti capitis ṗme partis: igit̄̄ correlariū verum.</s>
                </p>
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                  <s xml:id="N2BB4B" xml:space="preserve">Secūda cõcluſio. </s>
                  <s xml:id="N2BB4E" xml:space="preserve">diuiſo corpore qua
                    <lb/>
                  volueris ꝓportiõe: et in q̈cū ꝓportiõe ſe habuerīt
                    <lb/>
                  ꝑtes aliq̄ proportiõalis ī eadē vel maiori ſe habue­
                    <lb/>
                  rit intēſio mīoris ad intēſionē maioris: totū illud
                    <lb/>
                  corpꝰ eſt īfinite intēſuꝫ. </s>
                  <s xml:id="N2BB59" xml:space="preserve">Exēplum / vt ſi diuiſo corꝑe
                    <lb/>
                  ꝓportõe dupla: et prīa ꝑs ꝓportionalis ſit aliq̈liṫ
                    <lb/>
                  alba: et ſcḋa ī duplo plꝰ: et tertia ī duplo plꝰ ꝙ̄ .2. et
                    <lb/>
                  4. in duplo plꝰ ꝙ̄ .3. / et ſic ↄ̨ñter: totū illḋ corpꝰ ē infi-
                    <lb/>
                  nire albū q2 q̄lꝫ ꝑs tm̄ denoīat ſicut prima: et ſunt
                    <lb/>
                  infinite </s>
                  <s xml:id="N2BB66" xml:space="preserve">(Sꝑ aūt ītelligo ſine ↄ̈rii ꝑmixtiõe) </s>
                  <s xml:id="N2BB69" xml:space="preserve">Proba­
                    <lb/>
                  tur ↄ̨° facile: qm̄ ex caſu ↄ̨°nis cõtinuo talis eſt pro-
                    <lb/>
                  portio ꝑtiū ſubiecti q̈lis eſt proportio intenſionis </s>
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